# CARLETON UNIVERSITY Department of Civil and Environmental Engineering

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```					                                   CARLETON UNIVERSITY
Department of Civil and Environmental Engineering
CIVE 5708 / ENVE 5402 – Finite Element in field problems (Fall 2008)

Assignment 2
(Due Date: Oct. 15, 2008)

1- The elliptic differential equation Dd2Φ/dx2 = 0 governs the heat transfer in each section of
the composite wall shown in the figure below, where D is the thermal conductivity. By
using Galarkin’s method and element formulation, calculate the nodal temperature
values within the wall and evaluate the heat flux through each material, assuming a unit
of surface area. The heat flux can be calculated given by q = - D dΦ/dx.
2- The beam shown in figure has been reinforced over the center one-half of its span
through the use of steel plates that are welded to the base section. The beam data, its
bending moment diagram, and the finite element mesh are given in the figure. The
governing differential equation for the deflection curve is:

EI d2v/dx2 – M(x) = 0

Calculate the nodal deflections of the beam.

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